Use our free GCF of Fractions Calculator tool to compute the GCF of 705/209, 320/629 i.e 5/131461 easily. The following is the detailed procedure to determine the greatest common factor of fractions 705/209, 320/629.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 705/209,320/629
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 705/209,320/629, numerators are 705,320
Denominators are 209,629
The GCF of 705,320 is 5 .
LCM of 209,629 is 131461.
The greatest common factor of 705/209,320/629 = [GCF of 705,320]/[LCM of 209,629]= 5/131461
Therefore, the GCF of 705/209,320/629 is 5/131461.
To find the highest common factor of 705,320, we have to find the factors of both numbers and list the highest common factor.
The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705
The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
The HCF of 705,320 is 5.
Lets's calculate GCF of 705,320
5 | 705, 320 |
141, 64 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 705
:1,3,5,15,47,141,235,705
Now, list down the factors of 320
:1,2,4,5,8,10,16,20,32,40,64,80,160,320
Greatest Common Factor
We found the factors 705,320 . The biggest common factor number is the GCF number.
So the greatest common factor 705,320 is 5.
Lets's calculate LCM of 209,629
Given numbers has no common factors except 1. So, there LCM is their product i.e 131461
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/131461
Therefore, the GCF of Fractions 705/209,320/629 is 5/131461
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 209,629 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(209,629) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(209,629) x common factors =1 x 1 = 1
LCM(209,629) = ( 209 × 629 ) / 1
LCM(209,629) = 131461 / 1
LCM(209,629) = 131461
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 705,320?
The HCF of 705,320 is 5
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 705/209, 320/629?
Answer: GCF of Numerators as per given numbers 705/209, 320/629 is
GCF of Numerators i.e. for 705,320 is 5
LCM of denominators i.e. for 209,629 is 131461.
Thus, GCF of Fractions is 5/131461.Finally, GCF of Fractions for 705/209, 320/629 is 5/131461.